Which law states that the effect of pressure is the same for all portions of a confined fluid?

$A$ hydraulic press containing water has two arms with diameters as shown in the figure. $A$ force of $10 \,N$ is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is . . . . . . $N$.

Why does the bottom of a bottle filled with liquid break when the cork is hit?

The movable cylindrical pistons $P_1$ and $P_2$ of a hydraulic lift are of radii $2 \,m$ and $R$ respectively. $A$ body of mass $32 \,kg$ on piston $P_2$ is supported by a body of mass $2 \,kg$ placed on piston $P_1$. The value of $R$ is (in $\,m$)

In a hydraulic lift,the surface area of the input piston is $6 \ cm^2$ and that of the output piston is $1500 \ cm^2$. If $100 \ N$ force is applied to the input piston to raise the output piston by $20 \ cm$,then the work done is . . . . . . $kJ$.

$A$ piston of cross-section area $100 \, cm^2$ is used in a hydraulic press to exert a force of $10^7 \, dynes$ on the water. The cross-sectional area of the other piston which supports an object having a mass $2000 \, kg$ is: